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ArithmeticQuestion and Answers: Page 1

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if the fraction ((m^2 +25m)/(m+1)) is reductible. how many values does m take if is a 2 digit number? thanks

$${if}\:{the}\:{fraction}\:\frac{{m}^{\mathrm{2}} +\mathrm{25}{m}}{{m}+\mathrm{1}}\:\:{is}\:{reductible}.\:{how}\:{many}\:{values}\:{does}\:{m}\:\:{take}\:{if}\:{is}\:{a}\:\mathrm{2}\:{digit}\:\:{number}?\:{thanks} \\ $$

Question Number 215845 Answers: 2 Comments: 10

1, 3, − 1, − 3, − 7, − 21, − 25, ___, ___, ___ Next three terms??

$$\mathrm{1},\:\mathrm{3},\:−\:\mathrm{1},\:−\:\mathrm{3},\:−\:\mathrm{7},\:\:−\:\mathrm{21},\:\:−\:\mathrm{25},\:\:\:\:\:\_\_\_,\:\:\:\:\:\_\_\_,\:\:\:\:\:\_\_\_ \\ $$$$ \\ $$$$\mathrm{Next}\:\mathrm{three}\:\mathrm{terms}?? \\ $$

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The two corner points of a square lie on curve f(x)= x^2 −2x−3 and the other two corner points lie on curve g(x)= −x^2 +2x+3 . It is known that the area of a square can be expressed by p+q(√r) , for a natural number p,q ,r where r is not divisible by any perfect square number other 1. The value of p+q+r =?

$$\:\:\mathrm{The}\:\mathrm{two}\:\mathrm{corner}\:\mathrm{points}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\: \\ $$$$\:\:\mathrm{lie}\:\mathrm{on}\:\mathrm{curve}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{3}\:\mathrm{and}\: \\ $$$$\:\mathrm{the}\:\mathrm{other}\:\mathrm{two}\:\mathrm{corner}\:\mathrm{points}\:\mathrm{lie}\:\mathrm{on}\: \\ $$$$\:\mathrm{curve}\:\mathrm{g}\left(\mathrm{x}\right)=\:−\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{3}\:.\:\mathrm{It}\:\mathrm{is}\:\mathrm{known} \\ $$$$\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\:\:\mathrm{expressed}\:\mathrm{by}\:\mathrm{p}+\mathrm{q}\sqrt{\mathrm{r}}\:,\:\mathrm{for}\:\mathrm{a}\:\mathrm{natural}\: \\ $$$$\:\mathrm{number}\:\mathrm{p},\mathrm{q}\:,\mathrm{r}\:\mathrm{where}\:\mathrm{r}\:\mathrm{is}\:\mathrm{not}\:\mathrm{divisible}\: \\ $$$$\:\mathrm{by}\:\mathrm{any}\:\mathrm{perfect}\:\mathrm{square}\:\mathrm{number}\:\mathrm{other}\:\mathrm{1}. \\ $$$$\:\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}+\mathrm{q}+\mathrm{r}\:=? \\ $$

Question Number 213261 Answers: 3 Comments: 0

if between 10^4 and 10^n there are 9999000 coprime numbers with 20. find n. please. thanks

$${if}\:{between}\:\:\mathrm{10}^{\mathrm{4}} \:{and}\:\mathrm{10}^{{n}} \:{there}\:{are}\:\mathrm{9999000}\:{coprime}\:{numbers}\:{with}\:\mathrm{20}.\:{find}\:{n}.\:\:{please}.\:{thanks} \\ $$

Question Number 213100 Answers: 1 Comments: 1

Find this numeric expression using: The arithmetic division rule a÷b(c)=a÷b×c, The solvable incorrect syntax rule (a)b=a×b, where b is a number: 12÷4(10−8+1)2÷6×2=?

$$\mathrm{Find}\:\mathrm{this}\:\mathrm{numeric}\:\mathrm{expression}\:\mathrm{using}: \\ $$$$\mathrm{The}\:\mathrm{arithmetic}\:\mathrm{division}\:\mathrm{rule}\:{a}\boldsymbol{\div}{b}\left({c}\right)={a}\boldsymbol{\div}{b}×{c}, \\ $$$$\mathrm{The}\:\mathrm{solvable}\:\mathrm{incorrect}\:\mathrm{syntax}\:\mathrm{rule}\:\left({a}\right){b}={a}×{b},\:\mathrm{where}\:{b}\:\mathrm{is}\:\mathrm{a}\:\mathrm{number}: \\ $$$$\mathrm{12}\boldsymbol{\div}\mathrm{4}\left(\mathrm{10}−\mathrm{8}+\mathrm{1}\right)\mathrm{2}\boldsymbol{\div}\mathrm{6}×\mathrm{2}=? \\ $$

Question Number 213000 Answers: 2 Comments: 0

f(((x−3)/(x+1))) + f(((x+3)/(1−x))) = x , x≠ ± 1 f(x)=?

$$\:\:\:\mathrm{f}\left(\frac{\mathrm{x}−\mathrm{3}}{\mathrm{x}+\mathrm{1}}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{x}+\mathrm{3}}{\mathrm{1}−\mathrm{x}}\right)\:=\:\mathrm{x}\:,\:\mathrm{x}\neq\:\pm\:\mathrm{1} \\ $$$$\:\:\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$

Question Number 212496 Answers: 0 Comments: 0

If 1.1!+3.2!+...+(2n−1).n! = a.(n+1)!+b(1!+2!+...+(n+1)!)+c for a,b,c integers number find 2a−b+3c

$$\:\mathrm{If}\:\mathrm{1}.\mathrm{1}!+\mathrm{3}.\mathrm{2}!+...+\left(\mathrm{2n}−\mathrm{1}\right).\mathrm{n}!\: \\ $$$$\:=\:\mathrm{a}.\left(\mathrm{n}+\mathrm{1}\right)!+\mathrm{b}\left(\mathrm{1}!+\mathrm{2}!+...+\left(\mathrm{n}+\mathrm{1}\right)!\right)+\mathrm{c}\: \\ $$$$\:\mathrm{for}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{integers}\:\mathrm{number} \\ $$$$\:\mathrm{find}\:\mathrm{2a}−\mathrm{b}+\mathrm{3c}\: \\ $$

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